This document has nls (non-linear least squares) regression fits to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass vs. stand age relationships. We calculated the biomass of each FIA plot by summing alive tree biomass (as reported by FIA). Stand age is also reported by FIA, using tree-core age estimates from two trees from the dominant size class of the FIA plot.
We considered the following Michaelis-Menten functional form \(B = (1 + (yr-1990)* \tau/100) \times (1 - \alpha \cdot B_l) \times \left( \frac{A \cdot STDAGE_{t2}}{k+STDAGE_{t2}}\right)\), where \(B\) is the plot biomass, \(B_l\) is the calculated biomass loss (proportion) for the previous FIA plot census interval, \(STDAGE_{t2}\) is the stand age at the second of two FIA plot tree censuses, and \(yr\) is the measurement year (all FIA data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(\tau\): biomass productivity trend, \(A\): the Michaelis-Menten asymptote and \(k\): the Michaelis-Menten half-saturation constant.
Data have increasing variance in \(B\) with increasing \(STDAGE_{t2}\), thus, weighted-nls is the best approach. We explored a few weighting options and found that proportional weighting can be achieved by weighting observations by \(\frac {1} {meanG}^2\) in equal-sample sized stand age bins (n=20 where possible, else n=10) for each ecoprovince. These bins are also used to visualize data means in relation to nls model fit.
Model selection is used to determine the best fitting models, which is implemented in three parts. The first part selects the best model form using \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest).
model 1: simple model \(B = (1 + (yr-1990)* \tau/100) \times \left( \frac {A \cdot STDAGE_{t2}} {k+STDAGE_{t2}} \right)\)
model 2: alpha model \(B = (1 + (yr-1990)* \tau/100) \times (1 - \alpha \cdot B_l) \times \left( \frac {A \cdot STDAGE_{t2}} {k+STDAGE_{t2}} \right)\)
Then, model selection part two takes the best fitting model from part 1 and and adds the \(p\) and \(s\) parameters (individually then together) to modify the Micheaelis-Menten functional form. The \(p\) parameter allows for an intercept in the model (i.e., for the model to not be forced through the origin), and the \(s\) parameter increases model flexibility, with \(s\)>1 leading to more-sigmoidal shape.
sub-model a: p form \(pA + \left( \frac {(1-p) * A \cdot STDAGE_{t2}} {k+STDAGE_{t2}} \right)\)
sub-model b: s form \(\left( \frac {A \cdot STDAGE_{t2}^s} {k^s+STDAGE_{t2}^s} \right)\)
sub-model c: p and s together \(pA + \left( \frac {(1-p) *A \cdot STDAGE_{t2}^s} {k^s + STDAGE_{t1}^s} \right)\)
Lastly, model selection part 3, fits three similar models to model selection part one, but uses the Log-Normal functional form. The Log-Normal equation fits more of “hump-shaped” curve which allows for a decrease in biomass at old stand ages. Two Log-normal models are fitted: 1) the simple model, and 2) the \(\alpha\) model: account for growth compensation due to plot biomass loss.
model 4: simple model \(B = (1 + (yr-1990)* \tau/100) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(STDAGE_{t2} /c \right)} {d} \right]} ^2 \right)\)
model 5: alpha model \(B = (1 + (yr-1990)* \tau/100) \times (1 - \alpha \cdot B_l) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(STDAGE_{t2} /c \right)} {d} \right]} ^2 \right)\)
Note:
This analysis only uses plot biomass data from the same plot locations and measurement intervals for which we also have data on biomass growth (which is used in the growth vs. biomass analysis ). We use the second of the two plot measurements comprising a \(G\) interval
This includes the following plot-based filtering criteria (which were used for the growth vs. biomass analysis):
Below the model fitting procedure is implemented by ecoprovince:
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6880 1758.3
## 2 6879 1588.0 1 170.38 738.11 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 74579.98
## 2 2 73880.45
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.69176 0.17752 3.897 9.84e-05 ***
## alpha 0.83853 0.02819 29.742 < 2e-16 ***
## A 416.54207 27.03681 15.406 < 2e-16 ***
## k 188.16891 13.29611 14.152 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4805 on 6879 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 9.098e-06
## (1 observation deleted due to missingness)
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6879 1588.0
## 2 6878 1587.8 1 0.10967 0.475 0.4907
## model AIC
## 1 2 73880.45
## 2 2a 73881.97
## 3 2b 73864.22
## 4 2c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.64525 0.17419 3.704 0.000214 ***
## alpha 0.84366 0.02836 29.752 < 2e-16 ***
## A 267.35244 24.48232 10.920 < 2e-16 ***
## k 87.16041 11.89186 7.329 2.58e-13 ***
## s 1.22609 0.05764 21.273 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4799 on 6878 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 5.167e-06
## (1 observation deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6878 1726.3
## 2 6877 1557.0 1 169.29 747.71 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2b 73864.22
## 2 3 74457.48
## 3 4 73749.07
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.81288 0.18481 4.398 1.11e-05 ***
## alpha 0.83154 0.02775 29.971 < 2e-16 ***
## a 31.22968 1.70998 18.263 < 2e-16 ***
## b 112.93234 5.39611 20.928 < 2e-16 ***
## c 123.66007 5.88096 21.027 < 2e-16 ***
## d 1.06739 0.04852 21.999 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4758 on 6877 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)
## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 21456 6780.2
## 2 21455 6542.2 1 237.98 780.44 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 223452.5
## 2 2 222687.8
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.95393 0.10285 9.275 <2e-16 ***
## alpha 0.76407 0.02559 29.853 <2e-16 ***
## A 167.63507 4.38459 38.233 <2e-16 ***
## k 78.56108 2.47525 31.739 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5522 on 21455 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 2.327e-06
## (1226 observations deleted due to missingness)
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 21455 6542.2
## 2 21454 6515.0 1 27.151 89.409 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 222687.8
## 2 2a 222600.5
## 3 2b 222539.7
## 4 2c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.06559 0.10698 9.961 <2e-16 ***
## alpha 0.76996 0.02564 30.034 <2e-16 ***
## A 115.78050 3.70206 31.275 <2e-16 ***
## k 40.57330 1.64862 24.610 <2e-16 ***
## s 1.41290 0.04066 34.748 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5503 on 21454 degrees of freedom
##
## Number of iterations to convergence: 11
## Achieved convergence tolerance: 4.417e-06
## (1226 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 21454 6676.2
## 2 21453 6430.8 1 245.39 818.61 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2b 222539.7
## 2 3 223124.9
## 3 4 222323.3
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.07103 0.10677 10.03 <2e-16 ***
## alpha 0.77321 0.02528 30.59 <2e-16 ***
## a 22.95843 0.83356 27.54 <2e-16 ***
## b 67.52314 1.55360 43.46 <2e-16 ***
## c 103.10031 2.16612 47.60 <2e-16 ***
## d 1.08732 0.02951 36.85 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5475 on 21453 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1226 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6934 1078.14
## 2 6933 950.93 1 127.21 927.46 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 75745.30
## 2 2 74876.34
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.16754 0.11201 1.496 0.135
## alpha 0.88651 0.02699 32.844 <2e-16 ***
## A 438.44852 23.33717 18.788 <2e-16 ***
## k 125.86939 8.34455 15.084 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3704 on 6933 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 3.061e-06
## (370 observations deleted due to missingness)
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6933 950.93
## 2 6932 944.77 1 6.1579 45.182 1.938e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 74876.34
## 2 2a 74833.27
## 3 2b NA
## 4 2c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.19985 0.11340 1.762 0.07805 .
## alpha 0.88716 0.02706 32.787 < 2e-16 ***
## A 297.82149 16.82169 17.705 < 2e-16 ***
## k 36.53118 7.80982 4.678 2.96e-06 ***
## p -0.36908 0.11916 -3.097 0.00196 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3692 on 6932 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 4.535e-06
## (370 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6932 1067.83
## 2 6931 941.94 1 125.89 926.36 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2a 74833.27
## 2 3 75682.64
## 3 4 74814.41
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.19868 0.11312 1.756 0.0791 .
## alpha 0.88629 0.02701 32.817 < 2e-16 ***
## a 46.50096 10.46650 4.443 9.02e-06 ***
## b 143.42164 12.84562 11.165 < 2e-16 ***
## c 119.23589 8.07145 14.773 < 2e-16 ***
## d 1.10698 0.12085 9.160 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3686 on 6931 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (370 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5547 1704.0
## 2 5546 1616.1 1 87.972 301.9 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 59908.34
## 2 2 59616.16
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.97722 0.20650 4.732 2.28e-06 ***
## alpha 0.83417 0.04432 18.822 < 2e-16 ***
## A 365.92255 32.26558 11.341 < 2e-16 ***
## k 190.74942 19.15547 9.958 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5398 on 5546 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 4.557e-06
## (296 observations deleted due to missingness)
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5546 1616.1
## 2 5545 1585.5 1 30.557 106.87 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 59616.16
## 2 2a 59512.21
## 3 2b NA
## 4 2c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.06896 0.21114 5.063 4.26e-07 ***
## alpha 0.86162 0.04368 19.726 < 2e-16 ***
## A 194.67994 12.87743 15.118 < 2e-16 ***
## k 40.40127 6.99591 5.775 8.11e-09 ***
## p -0.33156 0.07736 -4.286 1.85e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5347 on 5545 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 4.118e-06
## (296 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5545 1667.1
## 2 5544 1570.6 1 96.455 340.47 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2a 59512.21
## 2 3 59790.56
## 3 4 59461.77
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.06254 0.20963 5.069 4.14e-07 ***
## alpha 0.87213 0.04334 20.125 < 2e-16 ***
## a 19.41594 3.70394 5.242 1.65e-07 ***
## b 96.66094 5.38215 17.960 < 2e-16 ***
## c 101.25661 4.50967 22.453 < 2e-16 ***
## d 1.02471 0.07125 14.382 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5323 on 5544 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (296 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 9432 1587.5
## 2 9431 1471.4 1 116.06 743.86 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 98445.42
## 2 2 97731.13
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.9572 0.1106 8.651 <2e-16 ***
## alpha 0.7909 0.0270 29.288 <2e-16 ***
## A 179.3531 5.9484 30.152 <2e-16 ***
## k 52.8587 2.8565 18.505 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.395 on 9431 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 5.096e-07
## (571 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 9431 1471.4
## 2 9430 1465.8 1 5.5843 35.925 2.126e-09 ***
## 3 9430 1465.3 0 0.0000
## 4 9429 1465.2 1 0.0872 0.561 0.4539
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 97731.13
## 2 2a 97697.26
## 3 2b 97693.91
## 4 2c 97695.35
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.96491 0.11082 8.707 <2e-16 ***
## alpha 0.79208 0.02697 29.372 <2e-16 ***
## A 128.12523 4.67964 27.379 <2e-16 ***
## k 32.43433 0.96401 33.645 <2e-16 ***
## s 1.85487 0.14913 12.438 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3942 on 9430 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 1.503e-06
## (571 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 9430 1580.5
## 2 9429 1464.6 1 115.85 745.85 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2b 97693.91
## 2 3 98407.53
## 3 4 97691.25
## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Ecoprovince == "223", :
## provided 32 variables to replace 31 variables
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.95467 0.11054 8.637 < 2e-16 ***
## alpha 0.79131 0.02698 29.328 < 2e-16 ***
## a 14.36005 24.74403 0.580 0.562
## b 100.63809 25.72856 3.912 9.24e-05 ***
## c 118.73960 12.04638 9.857 < 2e-16 ***
## d 1.55264 0.35970 4.316 1.60e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3941 on 9429 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (571 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12112 2738.8
## 2 12111 2512.1 1 226.69 1092.9 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 130399.6
## 2 2 129354.9
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.31050 0.12159 10.78 <2e-16 ***
## alpha 0.71119 0.01999 35.59 <2e-16 ***
## A 278.85285 8.36741 33.33 <2e-16 ***
## k 76.76299 2.35893 32.54 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4554 on 12111 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 1.78e-06
## (729 observations deleted due to missingness)
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12111 2512.1
## 2 12110 2485.7 1 26.3813 128.5253 <2e-16 ***
## 3 12109 2485.6 1 0.0694 0.3383 0.5608
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 129354.9
## 2 2a 129229.0
## 3 2b NA
## 4 2c 129230.7
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.296348 0.120428 10.765 <2e-16 ***
## alpha 0.718309 0.020363 35.275 <2e-16 ***
## A 220.176569 6.649464 33.112 <2e-16 ***
## k 42.722737 2.304084 18.542 <2e-16 ***
## p -0.062849 0.007588 -8.283 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4531 on 12110 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 1.038e-06
## (729 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12110 2709.7
## 2 12109 2486.7 1 223.02 1086 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2a 129229.0
## 2 3 130274.4
## 3 4 129235.9
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.296348 0.120428 10.765 <2e-16 ***
## alpha 0.718309 0.020363 35.275 <2e-16 ***
## A 220.176569 6.649464 33.112 <2e-16 ***
## k 42.722737 2.304084 18.542 <2e-16 ***
## p -0.062849 0.007588 -8.283 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4531 on 12110 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 1.038e-06
## (729 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12427 4751.2
## 2 12426 4496.0 1 255.23 705.42 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 137630.1
## 2 2 136945.7
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.79958 0.13463 5.939 2.94e-09 ***
## alpha 0.66173 0.02305 28.704 < 2e-16 ***
## A 296.34997 11.52223 25.720 < 2e-16 ***
## k 81.84131 3.24704 25.205 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6015 on 12426 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 1.623e-06
## (737 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12426 4496.0
## 2 12425 4481.7 1 14.2985 39.6414 3.154e-10 ***
## 3 12425 4479.1 0 0.0000
## 4 12424 4479.0 1 0.1142 0.3168 0.5735
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 136945.7
## 2 2a 136908.1
## 3 2b 136901.1
## 4 2c 136902.8
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.79154 0.13392 5.911 3.5e-09 ***
## alpha 0.67002 0.02357 28.426 < 2e-16 ***
## A 206.16286 9.61009 21.453 < 2e-16 ***
## k 41.26733 2.85865 14.436 < 2e-16 ***
## s 1.22628 0.03283 37.347 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6004 on 12425 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 1.442e-06
## (737 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12425 4726.6
## 2 12424 4479.2 1 247.46 686.39 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2b 136901.1
## 2 3 137569.6
## 3 4 136903.2
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.79154 0.13392 5.911 3.5e-09 ***
## alpha 0.67002 0.02357 28.426 < 2e-16 ***
## A 206.16286 9.61009 21.453 < 2e-16 ***
## k 41.26733 2.85865 14.436 < 2e-16 ***
## s 1.22628 0.03283 37.347 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6004 on 12425 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 1.442e-06
## (737 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1273 342.72
## 2 1272 305.18 1 37.541 156.47 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 14240.14
## 2 2 14094.10
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.52561 0.40921 1.284 0.199
## alpha 0.79999 0.05788 13.821 < 2e-16 ***
## A 478.26877 81.98228 5.834 6.86e-09 ***
## k 153.20836 30.69689 4.991 6.84e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4898 on 1272 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 2.326e-06
## (68 observations deleted due to missingness)
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_234, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_234, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1272 305.18
## 2 1271 304.82 1 0.35578 1.4835 0.2235
## model AIC
## 1 2 14094.10
## 2 2a 14094.62
## 3 2b NA
## 4 2c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.52561 0.40921 1.284 0.199
## alpha 0.79999 0.05788 13.821 < 2e-16 ***
## A 478.26877 81.98228 5.834 6.86e-09 ***
## k 153.20836 30.69689 4.991 6.84e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4898 on 1272 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 2.326e-06
## (68 observations deleted due to missingness)
## Error in nls(f_3, data = G_234, start = c(tau = tau.start, a = a.start, :
## Convergence failure: iteration limit reached without convergence (10)
## model AIC
## 1 2 14094.10
## 2 3 NA
## 3 4 14096.77
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.52561 0.40921 1.284 0.199
## alpha 0.79999 0.05788 13.821 < 2e-16 ***
## A 478.26877 81.98228 5.834 6.86e-09 ***
## k 153.20836 30.69689 4.991 6.84e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4898 on 1272 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 2.326e-06
## (68 observations deleted due to missingness)
`## plotting 2
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2165 468.74
## 2 2164 449.79 1 18.948 91.16 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 22573.55
## 2 2 22486.10
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.30617 0.21270 1.439 0.15
## alpha 0.70921 0.06963 10.186 <2e-16 ***
## A 234.25380 19.13609 12.241 <2e-16 ***
## k 86.34944 9.58196 9.012 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4559 on 2164 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 3.498e-06
## (122 observations deleted due to missingness)
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2164 449.79
## 2 2163 442.07 1 7.7182 37.764 9.477e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 22486.10
## 2 2a 22450.57
## 3 2b 22453.39
## 4 2c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.40256 0.21862 1.841 0.0657 .
## alpha 0.71553 0.06967 10.270 <2e-16 ***
## A 148.57344 10.23035 14.523 <2e-16 ***
## k 5.24468 5.41531 0.968 0.3329
## p -3.23715 3.60610 -0.898 0.3695
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4521 on 2163 degrees of freedom
##
## Number of iterations to convergence: 18
## Achieved convergence tolerance: 8.969e-06
## (122 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2163 462.14
## 2 2162 443.26 1 18.877 92.069 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2a 22450.57
## 2 3 22546.83
## 3 4 22458.41
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.40256 0.21862 1.841 0.0657 .
## alpha 0.71553 0.06967 10.270 <2e-16 ***
## A 148.57344 10.23035 14.523 <2e-16 ***
## k 5.24468 5.41531 0.968 0.3329
## p -3.23715 3.60610 -0.898 0.3695
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4521 on 2163 degrees of freedom
##
## Number of iterations to convergence: 18
## Achieved convergence tolerance: 8.969e-06
## (122 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 708 336.70
## 2 707 329.96 1 6.7436 14.449 0.0001564 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 7311.058
## 2 2 7298.673
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.2620 0.4735 -0.553 0.58018
## alpha 0.4666 0.1144 4.077 5.07e-05 ***
## A 317.9208 75.0171 4.238 2.55e-05 ***
## k 133.3036 34.6376 3.849 0.00013 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6832 on 707 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 4.037e-06
## (3 observations deleted due to missingness)
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 707 329.96
## 2 706 329.85 1 0.10851 0.2322 0.63
## model AIC
## 1 2 7298.673
## 2 2a 7300.439
## 3 2b NA
## 4 2c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.2620 0.4735 -0.553 0.58018
## alpha 0.4666 0.1144 4.077 5.07e-05 ***
## A 317.9208 75.0171 4.238 2.55e-05 ***
## k 133.3036 34.6376 3.849 0.00013 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6832 on 707 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 4.037e-06
## (3 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 706 321.06
## 2 705 310.62 1 10.448 23.714 1.381e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 7298.673
## 2 3 7281.242
## 3 4 7259.720
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.3313 0.4397 -0.754 0.451
## alpha 0.5608 0.1051 5.333 1.30e-07 ***
## a 11.8038 1.9008 6.210 9.06e-10 ***
## b 88.9590 10.2328 8.693 < 2e-16 ***
## c 58.2985 5.0380 11.572 < 2e-16 ***
## d 1.0553 0.0947 11.143 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6638 on 705 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (3 observations deleted due to missingness)
add p model: does not fit
add s model: does not fit
add s+p model: does not fit
unable to fit model (only 64 observations)
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
add p model: does not fit
add s model: does not fit
add s+p model: does not fit
unable to fit model (0 observations)
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 155 28.883
## 2 154 27.554 1 1.3296 7.4314 0.007153 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 1995.769
## 2 2 1990.323
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.2518 2.1470 0.583 0.56070
## alpha 0.7269 0.2520 2.885 0.00448 **
## A 5419.6547 2776.6065 1.952 0.05276 .
## k 1453.0069 510.1242 2.848 0.00500 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.423 on 154 degrees of freedom
##
## Number of iterations to convergence: 12
## Achieved convergence tolerance: 4.387e-06
## (1 observation deleted due to missingness)
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_263, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_263, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 154 27.554
## 2 153 26.681 1 0.87281 5.0051 0.02672 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 1990.323
## 2 2a 1987.237
## 3 2b NA
## 4 2c NA
## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Ecoprovince == "263", :
## provided 32 variables to replace 31 variables
## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Ecoprovince == "263", :
## provided 32 variables to replace 31 variables
## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Ecoprovince == "263", :
## provided 32 variables to replace 31 variables
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.752e+00 2.562e+00 0.684 0.495280
## alpha 8.326e-01 2.442e-01 3.410 0.000831 ***
## A 1.590e+04 2.006e+04 0.793 0.429275
## k 5.997e+03 7.916e+03 0.758 0.449878
## p 2.363e-03 2.414e-03 0.979 0.329190
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4176 on 153 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 5.066e-06
## (1 observation deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 153 30.979
## 2 152 29.287 1 1.6923 8.7832 0.00353 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2a 1987.237
## 2 3 2010.835
## 3 4 2003.960
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.752e+00 2.562e+00 0.684 0.495280
## alpha 8.326e-01 2.442e-01 3.410 0.000831 ***
## A 1.590e+04 2.006e+04 0.793 0.429275
## k 5.997e+03 7.916e+03 0.758 0.449878
## p 2.363e-03 2.414e-03 0.979 0.329190
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4176 on 153 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 5.066e-06
## (1 observation deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 214 67.657
## 2 213 67.621 1 0.036228 0.1141 0.7358
## model AIC
## 1 1 2322.942
## 2 2 2324.826
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.8160 0.9509 -0.858 0.3918
## A 277.8964 110.6751 2.511 0.0128 *
## k 159.0901 64.0178 2.485 0.0137 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5623 on 214 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 7.666e-06
## (1 observation deleted due to missingness)
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 214 67.657
## 2 213 67.505 1 0.15278 0.4821 0.4882
## model AIC
## 1 1 2322.942
## 2 1a 2324.452
## 3 1b NA
## 4 1c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.8160 0.9509 -0.858 0.3918
## A 277.8964 110.6751 2.511 0.0128 *
## k 159.0901 64.0178 2.485 0.0137 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5623 on 214 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 7.666e-06
## (1 observation deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 212 62.692
## 2 211 62.465 1 0.22643 0.7649 0.3828
## model AIC
## 1 1 2322.942
## 2 3 2310.402
## 3 4 2311.616
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b *
## exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.45035 0.59364 -2.443 0.015377 *
## a 40.15842 12.25407 3.277 0.001225 **
## b 148.91132 39.27593 3.791 0.000195 ***
## c 142.76710 8.69554 16.418 < 2e-16 ***
## d 0.64093 0.09421 6.803 1.03e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5438 on 212 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## Error in nls(f_1, data = G_322, start = c(tau = tau.start, A = A.start, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 1 NA
## 2 2 NA
## Warning in min(AIC1_322$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_322.", Mod.Sel1, sep = "")) :
## object 'nls_322.' not found
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 205 109.38
## 2 204 107.28 1 2.0903 3.9748 0.04752 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 2230.704
## 2 2 2228.690
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.4762 1.5880 0.300 0.765
## alpha 0.6443 0.2929 2.200 0.029 *
## A 502.5964 606.4813 0.829 0.408
## k 360.7593 468.4009 0.770 0.442
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7252 on 204 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 5.93e-06
## (24 observations deleted due to missingness)
## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = G_332, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_332, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_332, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## model AIC
## 1 2 2228.69
## 2 2a NA
## 3 2b NA
## 4 2c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.4762 1.5880 0.300 0.765
## alpha 0.6443 0.2929 2.200 0.029 *
## A 502.5964 606.4813 0.829 0.408
## k 360.7593 468.4009 0.770 0.442
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7252 on 204 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 5.93e-06
## (24 observations deleted due to missingness)
## Error in nls(f_3, data = G_332, start = c(tau = tau.start, a = a.start, :
## Convergence failure: iteration limit reached without convergence (10)
## Error in nls(f_4, data = G_332, start = c(tau = tau.start, alpha = alpha.start, :
## Convergence failure: iteration limit reached without convergence (10)
## model AIC
## 1 2 2228.69
## 2 3 NA
## 3 4 NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.4762 1.5880 0.300 0.765
## alpha 0.6443 0.2929 2.200 0.029 *
## A 502.5964 606.4813 0.829 0.408
## k 360.7593 468.4009 0.770 0.442
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7252 on 204 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 5.93e-06
## (24 observations deleted due to missingness)
simple log-normal model: does not fit
log-normal alpha model: does not fit
model not fitted because only 62 observations
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6772 1333.1
## 2 6771 1152.4 1 180.72 1061.8 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 71776.53
## 2 2 70791.58
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.83471 0.16884 4.944 7.84e-07 ***
## alpha 0.80612 0.02248 35.855 < 2e-16 ***
## A 416.13390 24.57826 16.931 < 2e-16 ***
## k 192.41525 11.49858 16.734 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4125 on 6771 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 1.492e-06
## (3 observations deleted due to missingness)
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6771 1152.4
## 2 6770 1144.3 1 8.0931 47.881 4.944e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 70791.58
## 2 2a 70745.83
## 3 2b NA
## 4 2c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.720852 0.161462 4.465 8.15e-06 ***
## alpha 0.814665 0.022641 35.982 < 2e-16 ***
## A 311.623953 18.279896 17.047 < 2e-16 ***
## k 106.277700 10.003747 10.624 < 2e-16 ***
## p -0.044463 0.009478 -4.691 2.77e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4111 on 6770 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 7.248e-06
## (3 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6770 1322.9
## 2 6769 1140.1 1 182.86 1085.7 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2a 70745.83
## 2 3 71728.53
## 3 4 70722.69
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.72103 0.16125 4.471 7.90e-06 ***
## alpha 0.81660 0.02244 36.392 < 2e-16 ***
## a 11.86910 2.87240 4.132 3.64e-05 ***
## b 156.98730 10.86890 14.444 < 2e-16 ***
## c 207.69052 26.59499 7.809 6.62e-15 ***
## d 1.72266 0.11349 15.179 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4104 on 6769 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (3 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7751 1167.8
## 2 7750 1080.3 1 87.472 627.52 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 85843.11
## 2 2 85241.40
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.91183 0.12119 7.524 5.91e-14 ***
## alpha 0.90018 0.03388 26.571 < 2e-16 ***
## A 223.88494 7.41504 30.193 < 2e-16 ***
## k 43.44403 2.42381 17.924 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3734 on 7750 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 4.246e-06
## (432 observations deleted due to missingness)
## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = G_M221, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7750 1080.3
## 2 7748 1066.6 2 13.731 49.874 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 85241.40
## 2 2a NA
## 3 2b 85154.38
## 4 2c 85146.21
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.99857 0.12481 8.001 1.41e-15 ***
## alpha 0.89771 0.03372 26.622 < 2e-16 ***
## A 154.79938 4.49176 34.463 < 2e-16 ***
## k 44.43699 2.39761 18.534 < 2e-16 ***
## p 0.40664 0.05999 6.779 1.30e-11 ***
## s 3.75774 0.53787 6.986 3.06e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.371 on 7748 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 9.783e-06
## (432 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7749 1151.2
## 2 7748 1064.1 1 87.036 633.71 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2c 85146.21
## 2 3 85736.15
## 3 4 85128.55
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.99348 0.12427 7.994 1.49e-15 ***
## alpha 0.89846 0.03365 26.700 < 2e-16 ***
## a 49.42999 12.68864 3.896 9.88e-05 ***
## b 102.10729 12.62474 8.088 6.99e-16 ***
## c 100.61164 3.18931 31.547 < 2e-16 ***
## d 1.10537 0.12889 8.576 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3706 on 7748 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (432 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 887 122.26
## 2 886 106.68 1 15.583 129.42 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 9055.244
## 2 2 8935.898
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.01094 0.25540 -0.043 0.966
## alpha 0.89519 0.07261 12.329 < 2e-16 ***
## A 292.54555 34.23433 8.545 < 2e-16 ***
## k 95.82504 15.20296 6.303 4.6e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.347 on 886 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 1.455e-06
## (3 observations deleted due to missingness)
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_M223, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 886 106.68
## 2 885 106.00 1 0.67604 5.6442 0.01773 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 8935.898
## 2 2a 8932.240
## 3 2b NA
## 4 2c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.04774 0.26180 0.182 0.8553
## alpha 0.90336 0.07277 12.413 < 2e-16 ***
## A 225.89814 25.25934 8.943 < 2e-16 ***
## k 51.43265 12.26266 4.194 3.01e-05 ***
## p -0.08665 0.04437 -1.953 0.0512 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3461 on 885 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 1.431e-06
## (3 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 885 121.92
## 2 884 106.29 1 15.629 129.98 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2a 8932.240
## 2 3 9056.791
## 3 4 8936.700
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.04774 0.26180 0.182 0.8553
## alpha 0.90336 0.07277 12.413 < 2e-16 ***
## A 225.89814 25.25934 8.943 < 2e-16 ***
## k 51.43265 12.26266 4.194 3.01e-05 ***
## p -0.08665 0.04437 -1.953 0.0512 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3461 on 885 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 1.431e-06
## (3 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 955 204.76
## 2 954 190.05 1 14.711 73.843 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 9951.187
## 2 2 9881.765
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.46206 0.43464 1.063 0.288
## alpha 0.77623 0.08421 9.218 < 2e-16 ***
## A 306.46634 52.06959 5.886 5.48e-09 ***
## k 133.47106 25.97517 5.138 3.36e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4463 on 954 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 1.065e-06
## (51 observations deleted due to missingness)
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_M231, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 954 190.05
## 2 953 189.87 1 0.18837 0.9455 0.3311
## model AIC
## 1 2 9881.765
## 2 2a 9882.815
## 3 2b 9883.524
## 4 2c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.46206 0.43464 1.063 0.288
## alpha 0.77623 0.08421 9.218 < 2e-16 ***
## A 306.46634 52.06959 5.886 5.48e-09 ***
## k 133.47106 25.97517 5.138 3.36e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4463 on 954 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 1.065e-06
## (51 observations deleted due to missingness)
## Error in nls(f_4, data = G_M231, start = c(tau = tau.start, alpha = alpha.start, :
## Convergence failure: singular convergence (7)
## model AIC
## 1 2 9881.765
## 2 3 9954.667
## 3 4 NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.46206 0.43464 1.063 0.288
## alpha 0.77623 0.08421 9.218 < 2e-16 ***
## A 306.46634 52.06959 5.886 5.48e-09 ***
## k 133.47106 25.97517 5.138 3.36e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4463 on 954 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 1.065e-06
## (51 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3298 2133.7
## 2 3297 2025.3 1 108.38 176.43 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 43707.67
## 2 2 43537.59
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 5.191e-01 6.682e-01 0.777 0.437
## alpha 1.013e+00 6.953e-02 14.570 < 2e-16 ***
## A 1.011e+03 1.753e+02 5.765 8.94e-09 ***
## k 3.764e+02 3.589e+01 10.485 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7838 on 3297 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 7.623e-06
## (2 observations deleted due to missingness)
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3297 2025.3
## 2 3296 1977.6 1 47.753 79.588 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 43537.59
## 2 2a 43460.83
## 3 2b 43454.65
## 4 2c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.53718 0.65998 0.814 0.416
## alpha 1.07143 0.06934 15.451 < 2e-16 ***
## A 536.31143 86.55496 6.196 6.5e-10 ***
## k 119.02407 10.27404 11.585 < 2e-16 ***
## s 1.45921 0.05940 24.566 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7739 on 3296 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 1.462e-06
## (2 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3296 2088.0
## 2 3295 1970.6 1 117.4 196.3 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2b 43454.65
## 2 3 43640.14
## 3 4 43451.11
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.5901 0.6749 0.874 0.382
## alpha 1.0753 0.0695 15.472 < 2e-16 ***
## a 0.0000 5.4149 0.000 1.000
## b 467.6358 77.2386 6.054 1.57e-09 ***
## c 581.4147 102.1728 5.691 1.38e-08 ***
## d 2.0957 0.1343 15.603 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7733 on 3295 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (2 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1983 1184.8
## 2 1982 1168.9 1 15.894 26.95 2.302e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 24895.19
## 2 2 24870.37
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 7.8534 4.3636 1.800 0.07205 .
## alpha 0.6133 0.1100 5.576 2.80e-08 ***
## A 145.3203 54.2373 2.679 0.00744 **
## k 128.1086 16.9324 7.566 5.86e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.768 on 1982 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 7.423e-06
## (7 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1982 1168.9
## 2 1981 1166.8 1 2.1673 3.6797 0.05522 .
## 3 1981 1168.2 0 0.0000
## 4 1980 1166.2 1 2.0169 3.4243 0.06439 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 24870.37
## 2 2a 24868.68
## 3 2b 24871.21
## 4 2c 24869.78
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 7.87846 4.37803 1.800 0.07208 .
## alpha 0.62355 0.11083 5.626 2.10e-08 ***
## A 130.60786 48.82237 2.675 0.00753 **
## k 90.96584 18.25938 4.982 6.84e-07 ***
## p -0.06446 0.03772 -1.709 0.08758 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7674 on 1981 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 6.152e-06
## (7 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1981 1182.3
## 2 1980 1166.2 1 16.138 27.4 1.83e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2a 24868.68
## 2 3 24894.97
## 3 4 24869.67
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 7.87846 4.37803 1.800 0.07208 .
## alpha 0.62355 0.11083 5.626 2.10e-08 ***
## A 130.60786 48.82237 2.675 0.00753 **
## k 90.96584 18.25938 4.982 6.84e-07 ***
## p -0.06446 0.03772 -1.709 0.08758 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7674 on 1981 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 6.152e-06
## (7 observations deleted due to missingness)
simple log-normal model: does not fit
log-normal alpha model: does not fit
model can fit - but K is negative (only 19 observations) - model excluded
## [1] "cannot plot data with prediction"
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 363 122.71
## 2 362 118.32 1 4.3863 13.419 0.0002862 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 3833.912
## 2 2 3822.590
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.9293 0.3039 -6.349 6.49e-10 ***
## alpha 0.5582 0.1420 3.930 0.000102 ***
## A 574.0776 210.6322 2.725 0.006732 **
## k 232.2820 111.8287 2.077 0.038495 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5717 on 362 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 9.569e-06
## (1 observation deleted due to missingness)
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_M313, :
## number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 362 118.32
## 2 361 116.79 1 1.5355 4.7465 0.03 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 3822.590
## 2 2a 3819.809
## 3 2b NA
## 4 2c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.94798 0.29564 -6.589 1.57e-10 ***
## alpha 0.59640 0.13334 4.473 1.04e-05 ***
## A 1027.37948 910.11547 1.129 0.260
## k 568.28926 621.17133 0.915 0.361
## p 0.02248 0.01655 1.358 0.175
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5688 on 361 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 7.979e-06
## (1 observation deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 361 120.72
## 2 360 115.26 1 5.4536 17.034 4.567e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2a 3819.809
## 2 3 3831.912
## 3 4 3816.992
## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Ecoprovince == "M313", :
## provided 32 variables to replace 31 variables
## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Ecoprovince == "M313", :
## provided 32 variables to replace 31 variables
## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Ecoprovince == "M313", :
## provided 32 variables to replace 31 variables
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.8271 0.3338 -5.473 8.29e-08 ***
## alpha 0.6108 0.1286 4.749 2.96e-06 ***
## a 42.6892 11.0490 3.864 0.000132 ***
## b 180.7375 41.0611 4.402 1.42e-05 ***
## c 177.7659 40.8862 4.348 1.79e-05 ***
## d 0.9807 0.2073 4.730 3.23e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5658 on 360 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1736 651.22
## 2 1735 600.64 1 50.579 146.1 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 18138.23
## 2 2 17999.63
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.85360 0.35023 -2.437 0.0149 *
## alpha 0.59310 0.04314 13.747 < 2e-16 ***
## A 274.07835 36.52316 7.504 9.82e-14 ***
## k 131.06768 13.53831 9.681 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5884 on 1735 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 4.714e-06
## (18 observations deleted due to missingness)
## Warning in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_M331, : No starting values specified for some parameters.
## Initializing 'tau', 'p', 'A', 's', 'k' to '1.'.
## Consider specifying 'start' or using a selfStart model
## Error in model.frame.default(formula = ~B_plt_t2_MgHa + MEASTIME_t2 + :
## variable lengths differ (found for '(sstart)')
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1735 600.64
## 2 1734 598.66 1 1.9884 5.7594 0.01651 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 17999.63
## 2 2a 17995.87
## 3 2b 18000.53
## 4 2c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.851806 0.350036 -2.433 0.01505 *
## alpha 0.596415 0.042420 14.060 < 2e-16 ***
## A 313.504594 50.186713 6.247 5.26e-10 ***
## k 179.346930 35.549874 5.045 5.01e-07 ***
## p 0.024058 0.008757 2.747 0.00607 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5876 on 1734 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 1.467e-06
## (18 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1734 645.18
## 2 1733 592.96 1 52.222 152.63 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2a 17995.87
## 2 3 18126.02
## 3 4 17981.24
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.87412 0.34288 -2.549 0.0109 *
## alpha 0.59872 0.04208 14.227 < 2e-16 ***
## a 27.03865 4.19436 6.446 1.48e-10 ***
## b 136.75568 18.11257 7.550 6.98e-14 ***
## c 241.17341 35.91839 6.714 2.55e-11 ***
## d 1.48402 0.13904 10.673 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5849 on 1733 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (18 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2617 1396.7
## 2 2616 1367.2 1 29.553 56.548 7.493e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 28732.83
## 2 2 28678.80
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.7345 0.8110 0.906 0.365
## alpha 0.4532 0.0565 8.021 1.56e-15 ***
## A 213.4846 40.2569 5.303 1.23e-07 ***
## k 149.0161 14.4932 10.282 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7229 on 2616 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 3.067e-06
## (1 observation deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2616 1367.2
## 2 2615 1366.1 1 1.0599 2.0289 0.1545
## 3 2615 1366.8 0 0.0000
## 4 2614 1351.0 1 15.7949 30.5617 3.554e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 28678.80
## 2 2a 28678.77
## 3 2b 28680.04
## 4 2c 28651.58
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.83577 0.84704 0.987 0.324
## alpha 0.45196 0.05499 8.218 3.21e-16 ***
## A 133.15226 26.79988 4.968 7.19e-07 ***
## k 75.15432 7.52220 9.991 < 2e-16 ***
## p 0.07982 0.01467 5.442 5.75e-08 ***
## s 1.75902 0.17763 9.903 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7189 on 2614 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 4.142e-06
## (1 observation deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2615 1381.0
## 2 2614 1348.8 1 32.212 62.43 4.031e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2c 28651.58
## 2 3 28707.13
## 3 4 28647.29
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.84900 0.84964 0.999 0.318
## alpha 0.45685 0.05461 8.365 < 2e-16 ***
## a 11.69323 2.46329 4.747 2.18e-06 ***
## b 104.61495 20.34549 5.142 2.92e-07 ***
## c 258.30931 37.51848 6.885 7.22e-12 ***
## d 1.65652 0.12460 13.294 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7183 on 2614 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1753 893.12
## 2 1752 852.89 1 40.224 82.628 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 19820.05
## 2 2 19741.13
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.49123 1.46753 1.016 0.309701
## alpha 0.60068 0.06033 9.957 < 2e-16 ***
## A 312.74968 91.61362 3.414 0.000655 ***
## k 219.15324 28.08087 7.804 1.02e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6977 on 1752 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 7.964e-06
## (2 observations deleted due to missingness)
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1752 852.89
## 2 1751 852.69 1 0.204 0.4189 0.5176
## model AIC
## 1 2 19741.13
## 2 2a 19742.70
## 3 2b NA
## 4 2c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.49123 1.46753 1.016 0.309701
## alpha 0.60068 0.06033 9.957 < 2e-16 ***
## A 312.74968 91.61362 3.414 0.000655 ***
## k 219.15324 28.08087 7.804 1.02e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6977 on 1752 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 7.964e-06
## (2 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1751 828.43
## 2 1750 790.40 1 38.027 84.194 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 19741.13
## 2 3 19692.03
## 3 4 19611.51
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 2.33449 1.85609 1.258 0.20865
## alpha 0.57698 0.05622 10.263 < 2e-16 ***
## a 12.02383 3.70753 3.243 0.00120 **
## b 93.63274 28.58260 3.276 0.00107 **
## c 137.55008 7.17906 19.160 < 2e-16 ***
## d 1.09309 0.05382 20.312 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6721 on 1750 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (2 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 424 163.07
## 2 423 146.44 1 16.63 48.035 1.57e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 4280.845
## 2 2 4236.917
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.2772 0.6406 0.433 0.66539
## alpha 0.8452 0.1103 7.661 1.27e-13 ***
## A 97.9714 18.4871 5.299 1.87e-07 ***
## k 53.0581 19.0692 2.782 0.00564 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5884 on 423 degrees of freedom
##
## Number of iterations to convergence: 4
## Achieved convergence tolerance: 1.825e-06
## (24 observations deleted due to missingness)
## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = G_M334, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_M334, :
## number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 2 4236.917
## 2 2a NA
## 3 2b NA
## 4 2c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.2772 0.6406 0.433 0.66539
## alpha 0.8452 0.1103 7.661 1.27e-13 ***
## A 97.9714 18.4871 5.299 1.87e-07 ***
## k 53.0581 19.0692 2.782 0.00564 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5884 on 423 degrees of freedom
##
## Number of iterations to convergence: 4
## Achieved convergence tolerance: 1.825e-06
## (24 observations deleted due to missingness)
## Error in nls(f_3, data = G_M334, start = c(tau = tau.start, a = a.start, :
## Convergence failure: singular convergence (7)
## Error in nls(f_4, data = G_M334, start = c(tau = tau.start, alpha = alpha.start, :
## Convergence failure: singular convergence (7)
## model AIC
## 1 2 4236.917
## 2 3 NA
## 3 4 NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.2772 0.6406 0.433 0.66539
## alpha 0.8452 0.1103 7.661 1.27e-13 ***
## A 97.9714 18.4871 5.299 1.87e-07 ***
## k 53.0581 19.0692 2.782 0.00564 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5884 on 423 degrees of freedom
##
## Number of iterations to convergence: 4
## Achieved convergence tolerance: 1.825e-06
## (24 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 214 80.493
## 2 213 77.386 1 3.1072 8.5523 0.003824 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 2156.928
## 2 2 2150.386
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.5816 0.5385 -2.937 0.003677 **
## alpha 0.4666 0.1455 3.207 0.001550 **
## A 235.0957 65.5828 3.585 0.000418 ***
## k 112.0187 30.9615 3.618 0.000371 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6028 on 213 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 3.283e-06
## (3 observations deleted due to missingness)
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 213 77.386
## 2 212 77.224 1 0.16244 0.4459 0.505
## model AIC
## 1 2 2150.386
## 2 2a 2151.930
## 3 2b 2152.190
## 4 2c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.5816 0.5385 -2.937 0.003677 **
## alpha 0.4666 0.1455 3.207 0.001550 **
## A 235.0957 65.5828 3.585 0.000418 ***
## k 112.0187 30.9615 3.618 0.000371 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6028 on 213 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 3.283e-06
## (3 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 212 76.519
## 2 211 72.714 1 3.805 11.041 0.00105 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 2150.386
## 2 3 2149.940
## 3 4 2140.872
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.5408 0.5351 -2.880 0.004391 **
## alpha 0.5053 0.1373 3.681 0.000295 ***
## a 22.4320 6.3018 3.560 0.000459 ***
## b 115.3948 27.5776 4.184 4.20e-05 ***
## c 156.2468 22.9600 6.805 1.03e-10 ***
## d 1.0795 0.2035 5.305 2.84e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.587 on 211 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (3 observations deleted due to missingness)
| Ecoprovince | Ecoregion | Sel.Mod.2 | Sel.Mod.3 | Best.Mod |
|---|---|---|---|---|
| 211 | Northeastern Mixed Forest | 2b | 4 | 4 |
| 212 | Laurentian Mixed Forest | 2b | 4 | 4 |
| 221 | Eastern Broadleaf Forest | 2a | 4 | 4 |
| 222 | Midwest Broadleaf Forest | 2a | 4 | 4 |
| 223 | Central Interior Broadleaf Forest | 2b | 4 | 4 |
| 231 | Southeastern Mixed Forest | 2a | 2a | 2a |
| 232 | Outer Coastal Plain Mixed Forest | 2b | 2b | 2b |
| 234 | Lower Mississippi Riverine Forest | 2 | 2 | 2 |
| 242 | Pacific Lowland Mixed Forest | NA | NA | NA |
| 251 | Prairie Parkland (Temperate) | 2a | 2a | 2a |
| 255 | Prairie Parkland (Subtropical) | 2 | 4 | 4 |
| 261 | California Coastal Chaparral Forest and Shrub | NA | NA | NA |
| 262 | California Dry Steppe | NA | NA | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | 2a | 2a | 2a |
| 313 | Colorado Plateau Semi-Desert | 1 | 3 | 3 |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | NA | NA | NA |
| 321 | Chihuahuan Semi-Desert | NA | NA | NA |
| 322 | American Semidesert and Desert | NA | NA | NA |
| 331 | Great Plains/Palouse Dry Steppe | NA | NA | NA |
| 332 | Great Plains Steppe | 2 | 2 | 2 |
| 341 | Intermountain Semi-Desert and Desert | NA | NA | NA |
| 342 | Intermountain Semi-Desert | NA | NA | NA |
| 411 | Everglades | NA | NA | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | 2a | 4 | 4 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | 2c | 4 | 4 |
| M223 | Ozark Broadleaf Forest Meadow | 2a | 2a | 2a |
| M231 | Ouachita Mixed Forest | 2 | 2 | 2 |
| M242 | Cascade Mixed Forest | 2b | 4 | 4 |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | 2a | 2a | 2a |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | NA | NA | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | 2a | 4 | 4 |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | 2a | 4 | 4 |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | 2c | 4 | 4 |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | 2 | 4 | 4 |
| M334 | Black Hills Coniferous Forest | 2 | 2 | 2 |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | 2 | 4 | 4 |
| Ecoprovince | Ecoregion | region | n.obs | n.plots | tau | tau.variance | tau.2.5 | tau.97.5 | alpha | alpha.variance | alpha.2.5 | alpha.97.5 | A | A.2.5 | A.97.5 | k | k.2.5 | k.97.5 | a | a.2.5 | a.97.5 | b | b.2.5 | b.97.5 | c | c.2.5 | c.97.5 | d | d.2.5 | d.97.5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 211 | Northeastern Mixed Forest | east | 6884 | 2879 | 0.8128805 | 0.0341550 | 0.4505946 | 1.1751665 | 0.8315403 | 0.0007698 | 0.7771511 | 0.8859295 | 267.35244 | 219.35952 | 315.3454 | 87.16041 | 63.848690 | 110.47212 | 31.22968 | 27.877587 | 34.58178 | 112.93234 | 102.35431 | 123.51038 | 123.6601 | 112.13157 | 135.18857 | 1.0673927 | 0.9722764 | 1.1625091 |
| 212 | Laurentian Mixed Forest | east | 22685 | 9493 | 1.0710340 | 0.0114002 | 0.8617530 | 1.2803150 | 0.7732144 | 0.0006389 | 0.7236709 | 0.8227579 | 115.78050 | 108.52419 | 123.0368 | 40.57330 | 37.341870 | 43.80472 | 22.95843 | 21.324590 | 24.59227 | 67.52314 | 64.47797 | 70.56831 | 103.1003 | 98.85456 | 107.34606 | 1.0873191 | 1.0294815 | 1.1451566 |
| 221 | Eastern Broadleaf Forest | east | 7307 | 3560 | 0.1986788 | 0.0127951 | -0.0230617 | 0.4204193 | 0.8862948 | 0.0007294 | 0.8333532 | 0.9392364 | 297.82149 | 264.84583 | 330.7972 | 36.53118 | 21.221548 | 51.84081 | 46.50096 | 25.983421 | 67.01851 | 143.42164 | 118.24029 | 168.60298 | 119.2359 | 103.41338 | 135.05839 | 1.1069755 | 0.8700791 | 1.3438719 |
| 222 | Midwest Broadleaf Forest | east | 5846 | 2589 | 1.0625381 | 0.0439447 | 0.6515814 | 1.4734947 | 0.8721285 | 0.0018779 | 0.7871746 | 0.9570824 | 194.67994 | 169.43512 | 219.9248 | 40.40127 | 26.686540 | 54.11599 | 19.41594 | 12.154770 | 26.67712 | 96.66094 | 86.10982 | 107.21207 | 101.2566 | 92.41588 | 110.09733 | 1.0247052 | 0.8850278 | 1.1643826 |
| 223 | Central Interior Broadleaf Forest | east | 10006 | 3860 | 0.9546737 | 0.0122188 | 0.7379941 | 1.1713534 | 0.7913140 | 0.0007280 | 0.7384252 | 0.8442028 | 128.12523 | 118.95212 | 137.2983 | 32.43433 | 30.544669 | 34.32400 | 14.36005 | -34.143582 | 62.86369 | 100.63809 | 50.20456 | 151.07162 | 118.7396 | 95.12609 | 142.35311 | 1.5526382 | 0.8475389 | 2.2577374 |
| 231 | Southeastern Mixed Forest | east | 12844 | 5935 | 1.2963478 | 0.0145029 | 1.0602901 | 1.5324056 | 0.7183089 | 0.0004146 | 0.6783943 | 0.7582235 | 220.17657 | 207.14256 | 233.2106 | 42.72274 | 38.206364 | 47.23911 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 232 | Outer Coastal Plain Mixed Forest | east | 13167 | 6463 | 0.7915440 | 0.0179347 | 0.5290391 | 1.0540489 | 0.6700200 | 0.0005556 | 0.6238177 | 0.7162223 | 206.16286 | 187.32559 | 225.0001 | 41.26733 | 35.663943 | 46.87072 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 234 | Lower Mississippi Riverine Forest | east | 1344 | 759 | 0.5256142 | 0.1674543 | -0.2771902 | 1.3284185 | 0.7999862 | 0.0033505 | 0.6864285 | 0.9135439 | 478.26877 | 317.43343 | 639.1041 | 153.20836 | 92.986251 | 213.43046 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 242 | Pacific Lowland Mixed Forest | west | 85 | 85 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 251 | Prairie Parkland (Temperate) | east | 2290 | 903 | 0.4025611 | 0.0477957 | -0.0261705 | 0.8312927 | 0.7155331 | 0.0048541 | 0.5789034 | 0.8521628 | 148.57344 | 128.51110 | 168.6358 | 5.24468 | -5.375071 | 15.86443 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 255 | Prairie Parkland (Subtropical) | east | 714 | 318 | -0.3313144 | 0.1933208 | -1.1945585 | 0.5319296 | 0.5607660 | 0.0110571 | 0.3543162 | 0.7672159 | 317.92075 | 170.63777 | 465.2037 | 133.30362 | 65.298767 | 201.30848 | 11.80379 | 8.071868 | 15.53571 | 88.95895 | 68.86844 | 109.04946 | 58.2985 | 48.40726 | 68.18973 | 1.0552552 | 0.8693319 | 1.2411786 |
| 261 | California Coastal Chaparral Forest and Shrub | west | 26 | 26 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 262 | California Dry Steppe | west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | west | 159 | 157 | 1.7516497 | 6.5664031 | -3.3107992 | 6.8140987 | 0.8326216 | 0.0596171 | 0.3502495 | 1.3149937 | 15896.57299 | -23729.49974 | 55522.6457 | 5997.12443 | -9642.323051 | 21636.57192 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 313 | Colorado Plateau Semi-Desert | west | 218 | 218 | -1.4503531 | 0.3524055 | -2.6205414 | -0.2801648 | NA | NA | NA | NA | 277.89641 | 59.74344 | 496.0494 | 159.09011 | 32.903856 | 285.27637 | 40.15842 | 16.002996 | 64.31384 | 148.91133 | 71.48995 | 226.33270 | 142.7671 | 125.62629 | 159.90790 | 0.6409271 | 0.4552203 | 0.8266338 |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | west | 4 | 4 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 321 | Chihuahuan Semi-Desert | west | 9 | 9 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 322 | American Semidesert and Desert | west | 3 | 3 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 331 | Great Plains/Palouse Dry Steppe | west | 331 | 255 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 332 | Great Plains Steppe | west | 232 | 128 | 0.4762293 | 2.5216695 | -2.6547219 | 3.6071806 | 0.6443436 | 0.0858053 | 0.0667941 | 1.2218931 | 502.59644 | -693.17910 | 1698.3720 | 360.75928 | -562.768438 | 1284.28699 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 341 | Intermountain Semi-Desert and Desert | west | 66 | 64 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 342 | Intermountain Semi-Desert | west | 124 | 123 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 411 | Everglades | east | 96 | 63 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | east | 6778 | 3008 | 0.7210269 | 0.0260032 | 0.4049164 | 1.0371373 | 0.8165966 | 0.0005035 | 0.7726088 | 0.8605844 | 311.62395 | 275.78961 | 347.4583 | 106.27770 | 86.667211 | 125.88819 | 11.86910 | 6.238289 | 17.49991 | 156.98730 | 135.68083 | 178.29377 | 207.6905 | 155.55597 | 259.82507 | 1.7226645 | 1.5001895 | 1.9451395 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | east | 8186 | 3765 | 0.9934830 | 0.0154443 | 0.7498705 | 1.2370956 | 0.8984551 | 0.0011323 | 0.8324930 | 0.9644173 | 154.79938 | 145.99431 | 163.6045 | 44.43699 | 39.737017 | 49.13696 | 49.42999 | 24.556832 | 74.30314 | 102.10729 | 77.35940 | 126.85518 | 100.6116 | 94.35973 | 106.86354 | 1.1053708 | 0.8527202 | 1.3580215 |
| M223 | Ozark Broadleaf Forest Meadow | east | 893 | 348 | 0.0477424 | 0.0685395 | -0.4660799 | 0.5615648 | 0.9033564 | 0.0052962 | 0.7605248 | 1.0461880 | 225.89814 | 176.32294 | 275.4733 | 51.43265 | 27.365362 | 75.49995 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M231 | Ouachita Mixed Forest | east | 1009 | 496 | 0.4620608 | 0.1889160 | -0.3909092 | 1.3150308 | 0.7762262 | 0.0070908 | 0.6109745 | 0.9414779 | 306.46634 | 204.28218 | 408.6505 | 133.47106 | 82.495978 | 184.44613 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M242 | Cascade Mixed Forest | west | 3303 | 3286 | 0.5900829 | 0.4555005 | -0.7331980 | 1.9133639 | 1.0753087 | 0.0048303 | 0.9390411 | 1.2115764 | 536.31143 | 366.60451 | 706.0184 | 119.02407 | 98.879928 | 139.16821 | 0.00000 | -10.616952 | 10.61695 | 467.63578 | 316.19522 | 619.07633 | 581.4147 | 381.08599 | 781.74336 | 2.0957100 | 1.8323621 | 2.3590578 |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | west | 1993 | 1828 | 7.8784574 | 19.1671377 | -0.7075676 | 16.4644824 | 0.6235532 | 0.0122832 | 0.4061984 | 0.8409080 | 130.60786 | 34.85927 | 226.3564 | 90.96584 | 55.156230 | 126.77545 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | west | 30 | 26 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | west | 367 | 367 | -1.8270607 | 0.1225249 | -2.4835133 | -1.1706081 | 0.5964045 | 0.0165444 | 0.3341790 | 0.8586300 | 1027.37948 | -762.41454 | 2817.1735 | 568.28926 | -653.279611 | 1789.85813 | 42.68917 | 20.960445 | 64.41789 | 180.73752 | 99.98778 | 261.48725 | 177.7659 | 97.36014 | 258.17169 | 0.9807269 | 0.5729790 | 1.3884749 |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | west | 1757 | 1757 | -0.8741218 | 0.1175653 | -1.5466199 | -0.2016237 | 0.5987195 | 0.0017710 | 0.5161802 | 0.6812588 | 313.50459 | 215.07174 | 411.9375 | 179.34693 | 109.621788 | 249.07207 | 27.03865 | 18.812107 | 35.26519 | 136.75568 | 101.23088 | 172.28048 | 241.1734 | 170.72545 | 311.62137 | 1.4840181 | 1.2113066 | 1.7567296 |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | west | 2621 | 2611 | 0.8489972 | 0.7218949 | -0.8170458 | 2.5150402 | 0.4568543 | 0.0029828 | 0.3497617 | 0.5639469 | 133.15226 | 80.60113 | 185.7034 | 75.15432 | 60.404252 | 89.90438 | 11.69323 | 6.863029 | 16.52342 | 104.61495 | 64.72005 | 144.50985 | 258.3093 | 184.74038 | 331.87824 | 1.6565189 | 1.4121862 | 1.9008515 |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | west | 1758 | 1747 | 2.3344926 | 3.4450582 | -1.3058885 | 5.9748736 | 0.5769754 | 0.0031608 | 0.4667081 | 0.6872428 | 312.74968 | 133.06615 | 492.4332 | 219.15324 | 164.077704 | 274.22878 | 12.02383 | 4.752172 | 19.29549 | 93.63274 | 37.57311 | 149.69237 | 137.5501 | 123.46966 | 151.63051 | 1.0930900 | 0.9875411 | 1.1986390 |
| M334 | Black Hills Coniferous Forest | west | 451 | 179 | 0.2772480 | 0.4103689 | -0.9819086 | 1.5364046 | 0.8451811 | 0.0121699 | 0.6283424 | 1.0620199 | 97.97135 | 61.63333 | 134.3094 | 53.05812 | 15.576023 | 90.54022 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | west | 220 | 220 | -1.5407977 | 0.2862822 | -2.5955330 | -0.4860625 | 0.5053432 | 0.0211720 | 0.2347287 | 0.7759577 | 235.09566 | 105.82124 | 364.3701 | 112.01875 | 50.988548 | 173.04894 | 22.43196 | 10.009441 | 34.85447 | 115.39477 | 61.03188 | 169.75766 | 156.2468 | 110.98635 | 201.50728 | 1.0795052 | 0.6783650 | 1.4806453 |
## tau alpha a b c
## tau 0.034154968 -3.293976e-05 -0.17390829 -0.793823844 -0.079889622
## alpha -0.006423996 7.697974e-04 0.00263179 0.005057415 -0.002472449
## a -0.550302776 5.547168e-02 2.92403993 1.052106639 -3.656498436
## b -0.796006558 3.378001e-02 0.11402171 29.117970738 18.900890109
## c -0.073504706 -1.515273e-02 -0.36360133 0.595598266 34.585699132
## d -0.085697703 3.471544e-03 -0.56240022 0.570005584 0.910961614
## d
## tau -7.684697e-04
## alpha 4.673493e-06
## a -4.666248e-02
## b 1.492417e-01
## c 2.599435e-01
## d 2.354297e-03
## tau alpha a b c
## tau 0.01140025 0.0004251389 -0.0437925935 -0.131046828 -0.025538513
## alpha 0.15752878 0.0006388922 -0.0002584548 -0.002546829 -0.001535693
## a -0.49204748 -0.0122668871 0.6948210451 -0.011936079 -0.551432166
## b -0.79000659 -0.0648555853 -0.0092169364 2.413666428 1.726771735
## c -0.11042226 -0.0280484538 -0.3054033536 0.513114744 4.692060723
## d -0.02407672 -0.0069386385 -0.6657573057 0.464024636 0.811153380
## d
## tau -7.585637e-05
## alpha -5.175181e-06
## a -1.637533e-02
## b 2.127243e-02
## c 5.184684e-02
## d 8.707130e-04
## tau alpha a b c
## tau 0.01279505 0.0001236697 -1.710918e-01 -3.834621e-01 -0.027801875
## alpha 0.04048267 0.0007293676 7.656677e-04 5.272259e-04 -0.001632104
## a -0.14451297 0.0027087298 1.095476e+02 -1.189418e+02 -59.265887462
## b -0.26390421 0.0015197371 -8.846638e-01 1.650099e+02 85.926507053
## c -0.03045101 -0.0074872641 -7.015394e-01 8.287447e-01 65.148239726
## d 0.02789528 0.0075874415 -9.289982e-01 9.309494e-01 0.901522674
## d
## tau 3.813172e-04
## alpha 2.476299e-05
## a -1.175035e+00
## b 1.445159e+00
## c 8.793516e-01
## d 1.460391e-02
## tau alpha a b c
## tau 0.04394466 0.0015084853 -0.179346620 -0.694574424 -0.027812045
## alpha 0.16605333 0.0018779363 -0.004808419 -0.009751327 -0.006264714
## a -0.23098100 -0.0299569781 13.719166707 -10.991568329 -9.067076591
## b -0.61561600 -0.0418087783 -0.551365984 28.967542723 15.126501182
## c -0.02941947 -0.0320564803 -0.542823246 0.623214684 20.337143839
## d 0.04421864 -0.0008452601 -0.865739099 0.679738516 0.852702873
## d
## tau 6.604526e-04
## alpha -2.609841e-06
## a -2.284726e-01
## b 2.606639e-01
## c 2.739844e-01
## d 5.076523e-03
## tau alpha a b c
## tau 0.01221880 0.0005246004 -0.17767176 -6.604723e-02 2.095623e-02
## alpha 0.17589552 0.0007279794 -0.01386273 9.500917e-03 2.994822e-03
## a -0.06495815 -0.0207643759 612.26706998 -6.327252e+02 -2.304800e+02
## b -0.02322334 0.0136864379 -0.99386905 6.619590e+02 2.509666e+02
## c 0.01573773 0.0092141415 -0.77322540 8.097366e-01 1.451153e+02
## d 0.05479186 0.0187823639 -0.97922104 9.843806e-01 8.797111e-01
## d
## tau 0.0021785960
## alpha 0.0001822872
## a -8.7156057856
## b 9.1101387099
## c 3.8119141288
## d 0.1293876360
## tau alpha A k p
## tau 0.01450285 0.0001949633 -0.556054599 -0.003391909 1.483923e-05
## alpha 0.07950344 0.0004146487 -0.002302665 -0.001079011 -1.496585e-06
## A -0.69439093 -0.0170060718 44.215374190 10.766491368 3.104088e-02
## k -0.01222416 -0.0229978476 0.702731089 5.308804758 1.667267e-02
## p 0.01623981 -0.0096862943 0.615239101 0.953681138 5.757142e-05
## tau alpha A k s
## tau 0.01793470 0.0001487194 -0.714972319 -0.006000287 -1.252955e-04
## alpha 0.04711369 0.0005555804 0.001985514 -0.001042707 -6.050837e-06
## A -0.55553898 0.0087654029 92.353919166 22.803429480 -2.345681e-01
## k -0.01567346 -0.0154749304 0.830065323 8.171851420 -8.801539e-02
## s -0.02849401 -0.0078182057 -0.743372435 -0.937699133 1.078127e-03
## tau alpha A k
## tau 0.167454328 0.001355136 -17.1873405 -0.07518848
## alpha 0.057211002 0.003350503 -0.1997146 -0.10347624
## A -0.512319070 -0.042085718 6721.0935598 2157.77792059
## k -0.005985614 -0.058235955 0.8574175 942.29920519
## tau alpha A k p
## tau 0.04779568 0.003696598 -1.5199537 -0.16251893 -0.106163461
## alpha 0.24269117 0.004854091 -0.0675872 -0.01053084 -0.006856526
## A -0.67958786 -0.094824393 104.6600399 42.91056877 28.320759668
## k -0.13727343 -0.027911676 0.7745522 29.32555886 19.521808318
## p -0.13466118 -0.027290521 0.7676727 0.99967431 13.003993123
## tau alpha a b c
## tau 0.19332077 0.007344857 -0.498615073 -4.19255053 -0.06671220
## alpha 0.15886342 0.011057077 0.000975675 -0.03706817 -0.02010617
## a -0.59660668 0.004881429 3.613067354 9.03537112 -1.87751391
## b -0.93184237 -0.034449620 0.464527443 104.71121089 8.74377683
## c -0.03011686 -0.037953596 -0.196059915 0.16960793 25.38122913
## d -0.03198883 -0.064081241 -0.427313399 0.11886019 0.83381407
## d
## tau -0.0013319170
## alpha -0.0006381029
## a -0.0769173197
## b 0.1151788166
## c 0.3978003365
## d 0.0089676615
## tau alpha A k p
## tau 6.5664031 0.07181837 -1.285430e+04 2.219144e+03 -6.258973e-04
## alpha 0.1147854 0.05961707 3.499880e+02 2.097498e+02 -3.616051e-05
## A -0.2500923 0.07146340 4.023169e+08 1.482250e+08 -4.322236e+01
## k 0.1093949 0.10851548 9.334968e-01 6.266846e+07 -1.793040e+01
## p -0.1011995 -0.06136043 -8.928191e-01 -9.384361e-01 5.825345e-06
## tau a b c d
## tau 0.3524055 -5.7246279 -22.06300480 0.5913954 0.001058122
## a -0.7869475 150.1621212 309.82373329 -14.2180384 -0.299473936
## b -0.9462740 0.6437364 1542.59841013 -15.3030414 -0.164524650
## c 0.1145671 -0.1334329 -0.04480790 75.6124585 0.544092506
## d 0.0189200 -0.2594093 -0.04446428 0.6641754 0.008875373
## tau alpha A k
## tau 2.5216695 0.069998493 -3.814150e+02 -109.227617
## alpha 0.1504831 0.085805282 4.572344e-01 3.437316
## A -0.3960375 0.002573738 3.678196e+05 274225.961775
## k -0.1468489 0.025052135 9.653247e-01 219399.393626
## tau alpha a b c
## tau 0.02600316 -2.761285e-05 -0.034764631 -0.873034738 -0.07981265
## alpha -0.00763118 5.035155e-04 0.002764817 -0.003385973 -0.03071582
## a -0.07505497 4.289581e-02 8.250688464 -19.708703824 -54.50843225
## b -0.49811855 -1.388326e-02 -0.631287579 118.133058667 249.18479349
## c -0.01861053 -5.147020e-02 -0.713540632 0.862056883 707.29367745
## d -0.01897962 -4.291364e-02 -0.868218914 0.838638992 0.95816406
## d
## tau -0.0003473411
## alpha -0.0001092842
## a -0.2830283113
## b 1.0344662314
## c 2.8919801589
## d 0.0128798583
## tau alpha a b c
## tau 0.01544427 0.0002536698 -0.196584244 -2.457777e-01 -0.033877302
## alpha 0.06066054 0.0011322901 0.000362471 1.665029e-03 -0.001163569
## a -0.12466659 0.0008489447 161.001490491 -1.533477e+02 -18.532972265
## b -0.15665222 0.0039194092 -0.957282318 1.593839e+02 20.752286053
## c -0.08547293 -0.0108421847 -0.457966364 5.154032e-01 10.171689408
## d 0.02572335 0.0068963954 -0.951579959 9.424641e-01 0.667187808
## d
## tau 4.120174e-04
## alpha 2.990925e-05
## a -1.556198e+00
## b 1.533528e+00
## c 2.742516e-01
## d 1.661150e-02
## tau alpha A k p
## tau 0.06853953 0.000325955 -4.03057365 -0.27242629 -8.957156e-04
## alpha 0.01710824 0.005296189 0.05919583 -0.01203524 -4.468643e-05
## A -0.60950072 0.032202330 638.03446216 254.39202464 8.047295e-01
## k -0.08485817 -0.013486158 0.82129016 150.37291073 5.087456e-01
## p -0.07711058 -0.013839115 0.71802949 0.93504024 1.968662e-03
## tau alpha A k
## tau 0.188915964 0.0001524564 -13.7273187 -0.7699364
## alpha 0.004165477 0.0070907629 -0.2150236 -0.2291201
## A -0.606550870 -0.0490405568 2711.2422008 1121.5829707
## k -0.068196498 -0.1047510125 0.8292563 674.7096641
## tau alpha a b c
## tau 0.455500485 0.0003265189 -0.069700462 -47.94614555 0.1435947
## alpha 0.006961115 0.0048302571 -0.001789894 0.09259516 -0.1525302
## a -0.019072122 -0.0047560897 29.321381165 -77.65294702 -327.1580595
## b -0.919760452 0.0172491868 -0.185665489 5965.80551129 2889.1880122
## c 0.002082373 -0.0214800434 -0.591330013 0.36610509 10439.2904028
## d 0.020769211 -0.0133973082 -0.787866075 0.30434551 0.9421937
## d
## tau 0.0018827235
## alpha -0.0001250618
## a -0.5730159677
## b 3.1573560191
## c 12.9299789035
## d 0.0180403195
## tau alpha A k p
## tau 19.1671377313 0.07485946 -209.0074296 -0.74797970 -8.433607e-05
## alpha 0.1542809916 0.01228319 -0.7054270 -0.04442519 -9.261757e-05
## A -0.9778319433 -0.13036996 2383.6239698 181.85591933 2.626134e-01
## k -0.0093567522 -0.02195268 0.2039964 333.40499318 6.009473e-01
## p -0.0005107549 -0.02215724 0.1426185 0.87262612 1.422474e-03
## tau alpha a b c
## tau 0.111425743 0.0002768889 -2.529440e+00 -10.4807058 -1.5065987
## alpha 0.006448933 0.0165443521 1.988780e-01 0.3286231 0.3070966
## a -0.685816618 0.1399388646 1.220807e+02 172.2963033 -0.3624131
## b -0.764658023 0.0622218146 3.797711e-01 1686.0134031 1062.0122181
## c -0.110389609 0.0583947139 -8.022387e-04 0.6325901 1671.6804443
## d -0.096351180 0.0339530989 -1.484090e-01 0.5268294 0.9183837
## d
## tau -0.0066685434
## alpha 0.0009054938
## a -0.3399891459
## b 4.4851989129
## c 7.7854190641
## d 0.0429894959
## tau alpha a b c
## tau 0.117565294 -0.000447291 -1.08948293 -5.45404960 0.02726223
## alpha -0.030998552 0.001770999 0.02985268 0.03820798 -0.02760001
## a -0.757556422 0.169125171 17.59267006 38.15338208 -45.61992825
## b -0.878212045 0.050126191 0.50221194 328.06526847 280.79535627
## c 0.002213630 -0.018259256 -0.30281113 0.43161140 1290.13088760
## d 0.009871542 -0.034677596 -0.44745292 0.37590998 0.92231721
## d
## tau 0.0004706267
## alpha -0.0002029131
## a -0.2609547462
## b 0.9467078193
## c 4.6062677563
## d 0.0193332096
## tau alpha a b c
## tau 0.72189485 0.001706874 -1.81860986 -16.50260979 -2.5940486
## alpha 0.03678362 0.002982773 0.01413437 -0.01779304 -0.1041115
## a -0.86893434 0.105063237 6.06779937 38.53960620 -15.6004142
## b -0.95465737 -0.016012970 0.76899504 413.93891216 265.7892705
## c -0.08137592 -0.050809308 -0.16880111 0.34819626 1407.6361975
## d -0.05324810 -0.094018080 -0.30457223 0.27345268 0.9094210
## d
## tau -0.0056373301
## alpha -0.0006398141
## a -0.0934842063
## b 0.6932384732
## c 4.2515034037
## d 0.0155261823
## tau alpha a b c
## tau 3.44505817 0.003520774 -6.729276173 -52.81352651 -0.15008650
## alpha 0.03373972 0.003160798 0.008731308 -0.02811251 -0.01063845
## a -0.97787912 0.041888617 13.745792939 102.87060477 -0.82618681
## b -0.99550903 -0.017494420 0.970743994 816.96483683 12.38096064
## c -0.01126357 -0.026358017 -0.031040308 0.06033722 51.53884559
## d -0.02568570 -0.098885667 -0.076109778 0.04570799 0.80089205
## d
## tau -0.0025656358
## alpha -0.0002991831
## a -0.0151855555
## b 0.0703070926
## c 0.3094187709
## d 0.0028960807
## tau alpha A k
## tau 0.41036895 0.008872732 -7.84008531 -0.31934954
## alpha 0.12555261 0.012169947 -0.03070134 0.07153567
## A -0.66201025 -0.015053731 341.77292767 264.57032727
## k -0.02614253 0.034005321 0.75048304 363.63262478
## tau alpha a b c
## tau 0.28628223 -0.01338815 -2.83343963 -13.916816713 -0.8430314
## alpha -0.18227141 0.01884558 0.23803779 0.987256814 0.1778299
## a -0.84033709 0.27515529 39.71243136 130.831786659 -5.8229042
## b -0.94316230 0.26077686 0.75282452 760.523358217 139.7773938
## c -0.06862364 0.05641925 -0.04024423 0.220753656 527.1637135
## d 0.04196025 0.06218896 -0.25485915 0.006191206 0.7517345
## d
## tau 0.004568621
## alpha 0.001737272
## a -0.326823523
## b 0.034744122
## c 3.512263217
## d 0.041409469
## OGR data source with driver: ESRI Shapefile
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings: PROVINCE_ PROVINCE_I
## Warning: Removed 12 rows containing missing values (`geom_point()`).
## Warning: Removed 12 rows containing missing values (`geom_point()`).